Type: Article
Publication Date: 2003-12-01
Citations: 988
DOI: https://doi.org/10.1109/tit.2003.820031
The purpose of this paper is to generalize a result by Donoho and Huo [1] and Elad and Bruckstein [2] on sparse representations of signals in a union of two orthonormal bases for R N .We consider general (redundant) dictionaries for R N , and derive sufficient conditions for having unique sparse representations of signals in such dictionaries.The special case where the dictionary is given by the union of L ≥ 2 orthonormal bases for R N is studied in more detail.In particular, it is proved that the result of Donoho and Huo, concerning the replacement of the ℓ 0 optimization problem with a linear programming problem when searching for sparse representations, has an analog for dictionaries that may be highly redundant.